{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hide": true
   },
   "source": [
    "## Probability and Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "hide": true
   },
   "outputs": [],
   "source": [
    "# The %... is an iPython thing, and is not part of the Python language.\n",
    "# In this case we're just telling the plotting library to draw things on\n",
    "# the notebook, instead of on a separate window.\n",
    "%matplotlib inline\n",
    "# See all the \"as ...\" contructs? They're just aliasing the package names.\n",
    "# That way we can call methods like plt.plot() instead of matplotlib.pyplot.plot().\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import time\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is probability?\n",
    "\n",
    "Suppose you were to flip a coin. Then you expect not to be able to say whether the next toss would yield a heads or a tails.  You might tell a friend that the odds of getting a heads is equal to to the odds of getting a tails, and that both are $1/2$.\n",
    "\n",
    "This intuitive notion of odds is a **probability**. \n",
    "\n",
    "Consider another example. If we were tossing a 'fair' six-sided dice, we may thus equivalently say that the odds of the dice falling on any one of its sides is $1/6$. Indeed if there are $C$ different equally likely possibilities, we'd expect that the probability of any one particular outcome would be $1/C$.\n",
    "\n",
    "The examples of the coin as well as the dice illustrate the notion of probability springing from **symmetry**. Here we think of probability of of the number 4 on the dice as the ratio:\n",
    "\n",
    "$$\\frac{Number\\: of\\: cases\\: for\\: number\\: 4}{number\\: of\\: possibilities} = \\frac{1}{6},$$\n",
    " assuming equally likely possibilities.\n",
    "\n",
    "\n",
    "\n",
    "#### Probability from a model\n",
    "\n",
    "But now think of an event like an election, say a presidential election. You cant exactly run multiple trials of the election: its a one-off event. But you still want to talk about the likelyhood of a candidate winning. However people do make **models** of elections, based on inputs such as race, age, income, sampling polls, etc. They assign likeyhoods of candidates winning and run large numbers of **simulations** of the election, making predictions based on that. Forecasters like Nate Silver, Sam Wang, And Drew Linzer, made incredibly successfull predictions of the 2012 elections.\n",
    "\n",
    "Or consider what a weather forecaster means when he or she says there is a 90% chance of rain today. Presumably, this conclusion has been made from many computer **simulations** which take in the weather conditions known in the past, and propagated using physics to the current day. The simulations give different results based on the uncertainty in the measurement of past weather, and the inability of the physics to capture the phenomenon exactly (all physics is some approximation to the natural world). But 90% of these simulations show rain.\n",
    "\n",
    "In all of these cases, there is either a model (a fair coin, an election forecasting model, a weather differential equation), or an experiment ( a large number of coin tosses) that is used to **estimate** a probability, or the odds, of an **event** $E$ occuring. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing a model\n",
    "\n",
    "We can test the model of a fair coin by having carried out a large number of coin flips. You would do, or imagine doing, a large number of flips or **trials** $N$, and finding the number of times you got heads $N_H$. Then the probability of getting heads would be \n",
    "$$\\frac{N_H}{N}.$$\n",
    "\n",
    "#### Probability as frequency\n",
    "\n",
    "But, if you didnt know about the fairness of the coin, you can think of another notion probability as a **relative frequency**: if there are multiple ways an **event** like the tossing of a coin can happen, lets look at multiple trials of the event and see the fraction of times one or other of these ways happened. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simulating the results of the model\n",
    "\n",
    "We dont have a coin right now. So let us **simulate** this process on a computer. To do this we will use a form of the **random number generator** built into `numpy`. In particular, we will use the function `np.random.choice`, which will with equal probability for all items pick an item from a list (thus if the list is of size 6, it will pick one of the six list items each time, with a probability 1/6). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Throws: H T T T T T T H T H H T H T T H H T T T H T T H T T T H H T T H T T T H H T T H\n",
      "Number of Heads: 15\n",
      "p1 = Number of Heads/Total Throws: 0.375\n"
     ]
    }
   ],
   "source": [
    "def throw_a_coin(N):\n",
    "    return np.random.choice(['H','T'], size=N)\n",
    "throws=throw_a_coin(40)\n",
    "print \"Throws:\",\" \".join(throws)\n",
    "print \"Number of Heads:\", np.sum(throws=='H')\n",
    "print \"p1 = Number of Heads/Total Throws:\", np.sum(throws=='H')/40."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that you do not necessarily get 20 heads.\n",
    "\n",
    "Now say that we run the entire process again, a second **replication** to obtain a second sample. Then we ask the same question: what is the fraction of heads we get this time? Lets call the odds of heads in sample 2, then, $p_2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Throws: T T H H H T T T H T H H T T H H T T T H H H H H T T T H H T T T T T T T T H T H\n",
      "Number of Heads: 17\n",
      "p2 = Number of Heads/Total Throws: 0.425\n"
     ]
    }
   ],
   "source": [
    "throws=throw_a_coin(40)\n",
    "print \"Throws:\",\" \".join(throws)\n",
    "print \"Number of Heads:\", np.sum(throws=='H')\n",
    "print \"p2 = Number of Heads/Total Throws:\", np.sum(throws=='H')/40."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do many more trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 1000 Throws: H T T H H H T T H H T H T T T T H T T T H H T T H T H T T T T H T T T T T T T H T T H H H T H T T T T T H H H H T T H H T H H H H H H T H H T H T T H H H H H H T T H T T T H H T H T H T H T T H T T H H H T T H T H T H T T T H H T T H T H T T H H T T T H H H H H T H T H H H H T H T T H H T H H H H H H T T H T T H H T H H H T H H T H T T H T T T T H H T T H H H T H T H T H T H T T T T H T T T H H T H T T H T H T T H T T T H H H H T H T H T T T H T H T H T T H H H T H H T H H T H T H T T T H H T H T T H T H T H H H H H H T H H H T H T T T T T H T H H T T T T H H H H H T T T H H T H H H T T T H T T T T T T H H H T H H T T H H T T T T H H T H T T T H T H T T T H T T H H H T H H T T H H T T H H H T H T T T H H H T T H H H H H T H H H H T H H H T H H H H T H H H H H H H H H H T T H T T H T T H H H T T T H H T T H H H T H T H H H H H H T H H H H H T H T H H H T T T T H H H H T H T H T H T H H T T T T H H T T T H T H H H T T H H T T T T H H T T T T H T T T H H H T H H H T H H T T T H T T T T H \n",
      "Number of Heads: 4929\n",
      "p for 10,000 = Number of Heads/Total Throws: 0.4929\n"
     ]
    }
   ],
   "source": [
    "throws=throw_a_coin(10000)\n",
    "print \"First 1000 Throws:\",\" \".join(throws)[:1000]\n",
    "print \"Number of Heads:\", np.sum(throws=='H')\n",
    "print \"p for 10,000 = Number of Heads/Total Throws:\", np.sum(throws=='H')/10000."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The larger number of trials we do, the closer we seem to get to half the tosses showing up heads. Lets see this more systematically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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lp4R2AEhLSwNQ2WNSm06dOkEQBFy4cMFp6A4AXLhwAYBt2Jmj9PR0MUne7tKlS5DJZIiO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\njNTZs2ftt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d152390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trials=[10, 20, 50, 70, 100, 200, 500, 800, 1000, 2000, 5000, 7000, 10000]\n",
    "plt.plot(trials, [np.sum(throw_a_coin(j)=='H')/np.float(j) for j in trials], 'o-', alpha=0.6);\n",
    "plt.xscale(\"log\")\n",
    "plt.axhline(0.5, 0, 1, color='r');\n",
    "plt.xlabel('number of trials');\n",
    "plt.ylabel('probability of heads from simulation');\n",
    "plt.title('frequentist probability of heads');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the true odds **fluctuate** about their long-run value of 0.5, in accordance with the model of a fair coin (which we encoded in our simulation by having `np.random.choice` choose between two possibilities with equal probability), with the fluctuations becoming much smaller as the number of trials increases. These **fluctations** are what give rise to probability distributions.\n",
    "\n",
    "Each finite length run is called a **sample**, which has been obtained from the **generative** model of our fair coin. Its called generative as we can use the model to generate, using simulation, a set of samples we can play with to understand a model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A simple Election Model\n",
    "\n",
    "In the last section, we made a simple simulation of a coin-toss on the computer from a fair-coin model which associated equal probability with heads and tails. Let us consider another model here, a table of probabilities that [PredictWise](http://www.predictwise.com/results/2012/president) made on October 2, 2012 for the US presidential elections. \n",
    "PredictWise aggregated polling data and, for each state, estimated the probability that the Obama or Romney would win. Here are those estimated probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Obama</th>\n",
       "      <th>Romney</th>\n",
       "      <th>Votes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>States</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>0.062</td>\n",
       "      <td>0.938</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Obama  Romney  Votes\n",
       "States                          \n",
       "Alabama     0.000   1.000      9\n",
       "Alaska      0.000   1.000      3\n",
       "Arizona     0.062   0.938     11\n",
       "Arkansas    0.000   1.000      6\n",
       "California  1.000   0.000     55"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictwise = pd.read_csv('predictwise.csv').set_index('States')\n",
    "predictwise.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row is the probability predicted by Predictwise that Romney or Obama would win a state. The votes column lists the number of electoral college votes in that state. \n",
    "\n",
    "Remember that simulation is used in different ways in the modelling process. Simulations might be used to propagate differential equations which describe the weather from different initial conditions. In this case they are used to create the model. In the coin flips case, they are used to illustrate the predictions of the model of a fair coin. This example is in the same spirit: we are given a (somehow obtained) list of win probabilities for the states of the US. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of the tossed coins, even though we had a model which said that the probability of heads was 0.5, there were sequences of flips in which more or less than half the flips were heads. Similarly, here, if the probability of Romney winning in Arizona is 0.938, it means that if somehow, there were 10000 replications with an election each, Romney would win in 938 of those Arizonas **on the average** across the replications. And there would be some samples with Romney winning more, and some with less. We can run these **simulated** universes on a computer though not in real life.\n",
    "\n",
    "#### Simulating the model\n",
    "\n",
    "To do this, \n",
    "we will assume that the outcome in each state is the result of an independent coin flip whose probability of coming up Obama is given by the Predictwise state-wise win probabilities. Lets write a function `simulate_election` that uses this **predictive model** to simulate the outcome of the election given a table of probabilities.\n",
    "\n",
    "In the code below, each column simulates a single outcome from the 50 states + DC by choosing a random number between 0 and 1. Obama wins that simulation if the random number is $<$ the win probability. If he wins that simulation, we add in the electoral votes for that state, otherwise we dont. We do this `n_sim` times and return a list of total Obama electoral votes in each simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def simulate_election(model, n_sim):\n",
    "    simulations = np.random.uniform(size=(51, n_sim))\n",
    "    obama_votes = (simulations < model.Obama.values.reshape(-1, 1)) * model.Votes.values.reshape(-1, 1)\n",
    "    #summing over rows gives the total electoral votes for each simulation\n",
    "    return obama_votes.sum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code takes the necessary probabilities for the Predictwise data, and runs 10000 simulations. If you think of this in terms of our coins, think of it as having 51 biased coins, one for each state, and tossing them 10,000 times each.\n",
    "\n",
    "We use the results to compute the number of simulations, according to this predictive model, that Obama wins the election (i.e., the probability that he receives 269 or more electoral college votes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9953\n"
     ]
    }
   ],
   "source": [
    "result = simulate_election(predictwise, 10000)\n",
    "print (result >= 269).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([328, 326, 332, ..., 334, 326, 290])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are roughly only 50 simulations in which Romney wins the election!\n",
    "\n",
    "#### Displaying the prediction\n",
    "\n",
    "Now, lets visualize the simulation. We will build a histogram from the result of `simulate_election`. We will **normalize** the histogram by dividing the frequency of a vote tally by the number of simulations. We'll overplot the \"victory threshold\" of 269 votes as a vertical black line and the result (Obama winning 332 votes) as a vertical red line.\n",
    "\n",
    "We also compute the number of votes at the 5th and 95th quantiles, which we call the spread, and display it (this is an estimate of the outcome's uncertainty). By 5th quantile we mean that if we ordered the number of votes Obama gets in each simulation in increasing order, the 5th quantile is the number below which 5\\% of the simulations lie. \n",
    "\n",
    "We also display the probability of an Obama victory    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_simulation(simulation):    \n",
    "    plt.hist(simulation, bins=np.arange(200, 538, 1), \n",
    "             label='simulations', align='left', normed=True)\n",
    "    plt.axvline(332, 0, .5, color='r', label='Actual Outcome')\n",
    "    plt.axvline(269, 0, .5, color='k', label='Victory Threshold')\n",
    "    p05 = np.percentile(simulation, 5.)\n",
    "    p95 = np.percentile(simulation, 95.)\n",
    "    iq = int(p95 - p05)\n",
    "    pwin = ((simulation >= 269).mean() * 100)\n",
    "    plt.title(\"Chance of Obama Victory: %0.2f%%, Spread: %d votes\" % (pwin, iq))\n",
    "    plt.legend(frameon=False, loc='upper left')\n",
    "    plt.xlabel(\"Obama Electoral College Votes\")\n",
    "    plt.ylabel(\"Probability\")\n",
    "    sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MMcaSk5OZUChkq1at4pUrLi5m5ubmTE9Pj0uTzLNwdHRkJSUlXLpkrLi3tzeXNmvWLN5x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\nKkk6cOCATpw4oQ4dOnh83mHDhql///4aM2aM+vf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jiouLNXfuXLVv314zZszQ4cOH9dpr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\n7SBghSt+7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c43ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_simulation(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model created by combining the probabilities we obtained from Predictwise with the simulation of a biased coin flip corresponding to the win probability in each states leads us to obtain a histogram of election outcomes. We are plotting the probabilities of a prediction, so we call this distribution over outcomes the **predictive distribution**. Simulating from our model and plotting a histogram allows us to visualize this predictive distribution. In general, such a set of probabilities is called a **probability distribution** or **probability mass function**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Variables\n",
    "\n",
    "From wikipedia: In probability theory, the **sample space** of an experiment or random trial is the set of all possible outcomes or results of that experiment. For one coin toss, [H,T] make up the sample space.\n",
    "\n",
    "A **random variable** is a mapping from a sample space to the set of real numbers. It assigns a real number to each outcome in the sample space.\n",
    "\n",
    "For example, consider the event of a coin toss that we have seen before. There are two outcomes in the sample space, a heads and a tails. We can ask the question, whats the probability of a heads or a tails? For an unbiased coin, these are, by symmettry, 1/2 each. The random variable here is the number of heads, and its probability is P(0)=1/2, and P(1)=1/2.\n",
    "\n",
    "Another random variable is the number of heads in two coin tosses. There,  P(0)=1/4, P(1)=1/2, P(2)=1/4.\n",
    "\n",
    "Random variables provide the link from events and sample spaces to data, and it is their **probability distribution** that we are interested in.\n",
    "\n",
    "A random variable is called **discrete** if it has a countable number of values ^[The technical definition of countable is that there is a 1-1 correspondence with the integers 1,2,3...]. The number of heads in 2 coin tosses is a discrete random variable.\n",
    "\n",
    "### Bernoulli Random Variables (in scipy.stats)\n",
    "\n",
    "The **Bernoulli Distribution** represents the distribution for coin flips. Let the random variable X represent such a coin flip, where X=1 is heads, and X=0 is tails. Let us further say that the probability of heads is p (p=0.5 is a fair coin). \n",
    "\n",
    "We then say:\n",
    "\n",
    "$$X \\sim Bernoulli(p),$$\n",
    "\n",
    "which is to be read as **X has distribution Bernoulli(p)**. The **probability distribution function (pdf)** or **probability mass function** associated with the Bernoulli distribution is\n",
    "\n",
    "\\begin{eqnarray}\n",
    "P(X = 1) &=& p \\\\\n",
    "P(X = 0) &=& 1 - p \n",
    "\\end{eqnarray}\n",
    "\n",
    "for p in the range 0 to 1. \n",
    "The **pdf**, or the probability that random variable $X=x$ may thus be written as \n",
    "\n",
    "$$P(X=x) = p^x(1-p)^{1-x}$$\n",
    "\n",
    "for x in the set {0,1}.\n",
    "\n",
    "The **mean**, or **expected value** of this distribution can be calculated analogously to the mean value of data by noting that X=1 happens with frequency p*N, and X=0 happens with frequency (1-p)*N, so we have\n",
    "\n",
    "$$\\frac{p \\times N \\times 1+(1-p) \\times N \\times 0}{N}$$\n",
    "\n",
    "and thus it is p. \n",
    "\n",
    "Let us engage in some term defining right now. $X$ is a random variable, and when we say $X=x$ we are asking \"what if the random variable X takes the value x. $P(X=x)$ asks: what is the probability that the random variable X takes the value x. Finally $p$ is a parameter of the Bernoulli distribution, and as we have seen, one of the things we want to do in data analysis is: having seen some data, what can we infer to be the values of p, so that we can make future predictions for X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import bernoulli\n",
    "#bernoulli random variable\n",
    "brv=bernoulli(p=0.3)\n",
    "brv.rvs(size=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: **some of the code, and ALL of the visual style for the distribution plots below was shamelessly stolen from https://gist.github.com/mattions/6113437/ **."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ivNC+i0AsdXWu3FXKpuZ12Kw2kyMTkZmI9PeTCKaWNLnr6rB71TciMhv8QxOj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\nCVKyAAAAEqRkAQAAJEjJAgAASND/A3GdP0lLIbLAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cdc4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "event_space=[0,1]\n",
    "plt.figure(figsize=(12,8))\n",
    "colors=sns.color_palette()\n",
    "for i, p in enumerate([0.1, 0.2, 0.5, 0.7]):\n",
    "    ax = plt.subplot(1, 4, i+1)\n",
    "    plt.bar(event_space, bernoulli.pmf(event_space, p), label=p, color=colors[i], alpha=0.5)\n",
    "    plt.plot(event_space, bernoulli.cdf(event_space, p), color=colors[i], alpha=0.5)\n",
    "\n",
    "    ax.xaxis.set_ticks(event_space)\n",
    "   \n",
    "    plt.ylim((0,1))\n",
    "    plt.legend(loc=0)\n",
    "    if i == 0:\n",
    "        plt.ylabel(\"PDF at $k$\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us parse the intent of the above code a bit. We run 10,000 simulations. In each one of these simulations, we toss 51 biased coins, and assign the vote to obama is the output of `np.random.uniform` is less than the probablity of an obama win. \n",
    "\n",
    "### Uniform Distribution (in numpy)\n",
    "\n",
    "The first thing to pick up on here is that `np.random.uniform` gives you a random number between 0 and 1, uniformly. In other words, the number is equally likely to be between 0 and 0.1, 0.1 and 0.2, and so on. This is a very intuitive idea, but it is formalized by the notion of the **Uniform Distribution**.\n",
    "\n",
    "We then say:\n",
    "\n",
    "$$X \\sim Uniform([0,1),$$\n",
    "\n",
    "which is to be read as **X has distribution Uniform([0,1])**. The **probability distribution function (pdf)** associated with the Uniform distribution is\n",
    "\n",
    "\\begin{eqnarray}\n",
    "P(X = x) &=& 1 \\, for \\, x \\in [0,1] \\\\\n",
    "P(X = x) &=& 0 \\, for \\, x \\notin [0,1]\n",
    "\\end{eqnarray}\n",
    "\n",
    "What assigning the vote to Obama when the random variable **drawn** from the Uniform distribution is less than the Predictwise probability of Obama winning (which is a Bernoulli Parameter) does for us is this: if we have a large number of simulations and $p_{Obama}=0.7$ , then 70\\% of the time, the random numbes drawn will be below 0.7. And then, assigning those as Obama wins will hew to the frequentist notion of probability of the Obama win. But remember, of course, that in 30% of the simulations, Obama wont win, and this will induce fluctuations and a distribution on the total number of electoral college votes that Obama gets. And this is what we see in the histogram below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Empirical Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an **empirical Probability Mass Function** or **Probability Density Function**.  The word **density** is strictly used when the random variable X takes on continuous values, as in the uniform distribution, rather than discrete values such as here, but we'll abuse the language and use the word probability distribution in both cases.\n",
    "\n",
    "Lets summarize: the way the density arose here that we did ran 10,000 tosses (for each state), and depending on the value, assigned the state to Obama or Romney, and then summed up the electoral votes over the states.\n",
    "\n",
    "There is a second, very useful question, we can ask of any such probability density: what is the probability that a random variable is less than some value. In other words: $P(X < x)$. This is *also* a probability distribution and is called the **Cumulative Distribution Function**, or CDF (sometimes just called the **distribution**, as opposed to the **density**). Its obtained by \"summing\" the probability density function for all $X$ less than $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Obama Win CDF at votes= 200  is  0.0\n",
      "Obama Win CDF at votes= 300  is  0.1485\n",
      "Obama Win CDF at votes= 320  is  0.4442\n",
      "Obama Win CDF at votes= 340  is  0.8365\n",
      "Obama Win CDF at votes= 360  is  0.9971\n",
      "Obama Win CDF at votes= 400  is  1.0\n",
      "Obama Win CDF at votes= 500  is  1.0\n"
     ]
    }
   ],
   "source": [
    "CDF = lambda x: np.float(np.sum(result < x))/result.shape[0]\n",
    "for votes in [200, 300, 320, 340, 360, 400, 500]:\n",
    "    print \"Obama Win CDF at votes=\", votes, \" is \", CDF(votes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hp8V9+umntWDBAm3bts2VeQAAgJv58adMHT+TI0lqGxmiT2aMpGwAcJjDVzh6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\nAAA4DYEDAAAAgNP8P2I+eJyEa7njAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c905390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "votelist=np.arange(0, 540, 5)\n",
    "plt.plot(votelist, [CDF(v) for v in votelist], '.-');\n",
    "plt.xlim([200,400])\n",
    "plt.ylim([-0.1,1.1])\n",
    "plt.xlabel(\"votes for Obama\")\n",
    "plt.ylabel(\"probability of Obama win\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binomial Distribution (in scipy.stats)\n",
    "\n",
    "Let us consider a population of coinflips, n of them to be precise, $x_1,x_2,...,x_n$. The distribution of coin flips is the binomial distribution. By this we mean that each coin flip represents a bernoulli random variable (or comes from a bernoulli distribution) with  mean $p=0.5$.\n",
    "\n",
    "At this point, you might want to ask the question, what is the probability of obtaining $k$ heads in $n$ flips of the coin. We have seen this before, when we flipped 2 coins. What happens when when we flip 3?\n",
    "\n",
    "(This diagram is taken from the Feynman Lectures on Physics, volume 1. The chapter on probability is http://www.feynmanlectures.caltech.edu/I_06.html)\n",
    "![3 coin flips](3flips.png)\n",
    "\n",
    "We draw a possibilities diagram like we did with the 2 coin flips, and see that there are different probabilities associated with the events of 0, 1,2, and 3 heads with 1 and 2 heads being the most likely. \n",
    "The probability of each of these events is given by the **Binomial Distribution**, the distribution of the number of successes in a sequence of $n$ independent yes/no experiments, or Bernoulli trials, each of which yields success with probability $p$. The Binomial distribution is an extension of the Bernoulli when $n>1$ or the Bernoulli is the a special case of the Binomial when $n=1$.   \n",
    "\n",
    "$$P(X = k; n, p) = {n\\choose k}p^k(1-p)^{n-k} $$\n",
    "\n",
    "where\n",
    "\n",
    "$${n\\choose k}=\\frac{n!}{k!(n-k)!}$$\n",
    "\n",
    "The expected value $E[X]=np$ and the variance is $Var[X]=np(1-p)$\n",
    "\n",
    "How did we obtain this? The $p^k(1-p)^{n-k}$ comes simply from multiplying the probabilities for each bernoulli trial; there are $k$ 1's or yes's, and $n-k$ 0's or no's. The ${n\\choose k}$ comes from counting the number of ways in which each event happens: this corresponds to counting all the paths that give the same number of heads in the diagram above.\n",
    "\n",
    "We show the distribution below for 200 trials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jfIY31TG8UY1YrLZaD5sEGN6IiIiIfFVttwmw41YB6qtdvyg1WGW13CbAzmqT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\njYiIiIiIyAYweCMiIiIiIrIB/w9YKz07dnmBlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dba3810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "plt.figure(figsize=(12,6))\n",
    "k = np.arange(0, 200)\n",
    "for p, color in zip([0.1, 0.3, 0.7, 0.7, 0.9], colors):\n",
    "    rv = binom(200, p)\n",
    "    plt.plot(k, rv.pmf(k), '.', lw=2, color=color, label=p)\n",
    "    plt.fill_between(k, rv.pmf(k), color=color, alpha=0.5)\n",
    "q=plt.legend()\n",
    "plt.title(\"Binomial distribution\")\n",
    "plt.tight_layout()\n",
    "q=plt.ylabel(\"PDF at $k$\")\n",
    "q=plt.xlabel(\"$k$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The various ways to get random numbers\n",
    "\n",
    "1. `np.random.choice` chooses items randomly from an array, with or without replacement\n",
    "2. `np.random.random` gives us uniform randoms on [0.0,1.0)\n",
    "3. `np.random.randint` gives us random integers in some range\n",
    "4. `np.random.randn` gives us random samples from a Normal distribution, which we talk about later.\n",
    "5. `scipy.stats.distrib` gives us stuff from a distribution. Here distrib could be `binom` for example, as above. `distrib.pdf` or `distrib.pmf` give us the density or mass function, while `cdf` gives us the cumulaive distribution function. Just using `distrib` as a function with its params creates a random variable generating object, from which random variables can be generated in the form `distrib(params).rvs(size)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
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 },
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